So you do some reverse-engineering. On the whole it isn't much work than other consoles of that generation. The only reason there hasn't been any activity is because nobody (outside of the Xbox backwards compatibility team) sat down and did the work (because there's no incentive to)
Not really[1]. It was based on the GeFroce 3 architecture (NV20) but the actual chip had been quite different from the ones you could get on a retail card (NV2A). Even if it had been a straight off-the-shelf device it does not mean you know how it works. Look at the open-source drivers for the off-the-shelf video cards to see what is possible through reverse-engineering and what is not.
I cannot speak for other consoles of that generation, as I have not touched the GC but PS2 devkits came with nice printed manuals, describing every register and every command for almost every device (if memory serves there was not printed IOP manual but it was pretty much the PS1 chipset so its documentation had been obtainable too).
1. https://github.com/espes/xqemu/blob/xbox/hw/xbox/nv2a.c#L708
There have been quite a few Xbox 360 and Xbox SDK's appearing on Ebay, even some of the early PowerPC based Mac Soft SDK's for the Xbox 360 have appeared online so some one has them, too bad that people who buy them either collect them or in the case of the 360 dev box to create free XBLA gold accounts :P
I vaguely recall somebody from MS saying on the Xbox developer newsgroups that providing the full information wasn't part of their deal with NVidia, and that was that.